Officials at the Southern Examining Group refused to give the percentage needed for a grade C, the equivalent of a pass in the old O-level exam, but said it was "nowhere near" the figure being quoted.
Mathematics papers are divided into three levels of difficulty, and the paper in question was the most difficult. It is understood that the true figure corresponds closely to last year's grade C passmark for the hardest level in several subjects: 38 per cent in double science and 42 per cent in biology.
The board says that the mark for grade C in the most demanding maths exam was lowered this year, because candidates had found the paper so difficult. The School Curriculum and Assessment Authority insisted that the original exam was changed because it was not hard enough. The authority has asked for a report from one of its officials who was an assessor at the meeting at which the decision to lower the grade C mark was taken. Ministers have yet to decide whether to request an inquiry into the marking of the paper.
The dispute is bound to fuel the controversy about exam standards which will intensify on Thursday with the publication of this year's A-level results. The pass rate is expected to rise again. GCSE results are out next week.
The examining group pointed out that changing the mark required to achieve different grades was common practice. The aim was to ensure that candidates were not penalised if a paper had been more difficult than in previous years. Marks for a grade might change but standards did not. In addition, the mark required to achieve each grade varied from subject to subject. In English, last year, a grade C in the most difficult paper required 65 per cent.
George Turnbull, a spokesman for the group, said: "There is no magic raw mark which says that you have a grade C or B. If the exam is easier this year than last year, more people would get 50 per cent."
A spokesman for the School Curriculum and Assessment Authority said: "We shall be scrutinising this year's results ... and checking that the Southern Examining Group's results are comparable in standard to those of other boards."
The official UCAS listings of places available this year through clearing will appear exclusively in 'The Independent' starting on Monday, 19 August.